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Speeding up the implementation of Stochastic Gradient Ascent in Python

Code Review Asked on January 2, 2022

I am implementing a time-dependent Recommender System which applies BPR (Bayesian Personalized Ranking), where Stochastic Gradient Ascent is used to learn the parameters of the model. Such that, one iteration involves sampling randomly the quadruple (i.e. userID, positive_item, negative_item, epoch_index) for $n$ times, where $n$ is the total number of positive feedbacks (i.e. the number of ratings given to all items). But, as my implementation takes too much time for learning the parameters (since it requires 100 iterations to learn the parameters), I was wondering if there is a way to improve my code and speed up the learning process of the parameters.

In the following, please find the code of my implementation (the update function named as updateFactors is the one that learns the parameters, and such that I guess is the one that should be improved in order to speed up the process of learning the parameter values):

class TVBPR:

    def __init__(self, iterations, K, K2, nUsers, nItems, imageFeatures, nBins,  userItems, list_of_items, nr_of_pos_events, max_timestamp, feat, asinToInt, userIDToInt,itemIdToInt, min_timestamp, test_per_user, val_per_user):
        print 'initialization started...'
        sys.setrecursionlimit(5000)
        self.nUsers = nUsers
        self.nItems = nItems + 1 + 1
        self.nr_of_pos_events = nr_of_pos_events

        self.K = K # number of non-visual factors
        self.K2 = K2 # number of visual factors

        self.userItems = userItems
        self.itemIdToInt = itemIdToInt
        self.list_of_items = list_of_items

        self.nBins = nBins # number of epochs 
        self.maxTime = max_timestamp
        self.minTime = min_timestamp
        self.min_in_seconds = min_timestamp

        self.userIDToInt = userIDToInt
        self.itemIdToInt = itemIdToInt
        self.feat = feat # a dictionary where each item ID is associated with the values of 4096 features (features describing certain item, with values ranging between 0 - 1)
        self.asinToInt = asinToInt
        self.test_per_user = test_per_user
        self.val_per_user= val_per_user

        # biases
        self.b_u = np.zeros(self.nUsers)
        self.b_i = np.zeros(self.nItems)

        self.bi_bin = np.zeros((self.nItems, nBins))

        #non - visual factors
        self.gamma_user = np.random.random((self.nUsers + 1, K))
        self.gamma_item = np.random.random((self.nItems, K))

        # visual factors
        self.theta_user = np.random.random((self.nUsers + 1, K2))
        self.theta_item_per_bin = []
        for b in range(self.nBins):
            theta_item = np.zeros((self.nItems, K2))
            self.theta_item_per_bin.append(theta_item)

        self.E = np.random.random((K2, imageFeatures))
        self.E_t = np.random.random((nBins, K2, imageFeatures)) # image features = 4096

        # visual bias
        self.betta_cnn = np.random.random(imageFeatures)
        self.betta_cnn_t = []
        for i in range(nBins):
            b_cnn = np.zeros(imageFeatures)
            self.betta_cnn_t.append(b_cnn)

        self.J_t = np.zeros((nBins, K2)) # weighting vector for the embedding matrix
        self.C_t = np.zeros((nBins, imageFeatures)) # wieghting vector for the visual bias

        self.betta_item_visual_per_bin = np.zeros((nBins, self.nItems))

        epochs = self.init_epoch()
        self.epochs = epochs
        print 'self.epochs = ', self.epochs

        print 'initialization finished...'

        print 'training started...'
        self.train(iterations)
        print 'training finished...'

        print 'getting visual features...'
        self.getVisualFactors()
        print 'visual features calculation finished...'
    
        print 'initialization of epochs started...' 

        # apply DP
        # 1. calculate pos_items_per_bin
        self.votes_per_bin = self.pos_item_per_bin()

        # 2 init DP
        self.memo, self.sol = self.dp_init()

        # DP
        # self.DP(1000)

        print 'evaluating using AUC...'

        auc = self.AUC_(self.test_per_user, self.val_per_user)
        print 'AUC: ', auc 
        print 'epochs: ', self.epochs
        print 'evaluation finished...'

    def train(self, nr_of_iterations):
        for i in range(nr_of_iterations):
            print 'iteration: ', i + 1
            start_one_iter = time.time()
            self.oneIteration()
            end_time_iter = time.time()
            time_elapsed_one_iter = end_time_iter - start_one_iter
            print 'time elapsed in one iteration: ', time_elapsed_one_iter, 'sec.'

    def oneIteration(self):

        pos_per_user = {}
        for k,v in self.userItems.items():
            itemID = self.userItems[k][0][0]
            pos_per_user[k] = [(itemID, self.userItems[k][0][2])]
            for i in range(1, len(self.userItems[k])):
                pos_per_user[k].append((self.userItems[k][i][0], self.userItems[k][i][2]))

        for i in range(self.nr_of_pos_events): #self.nr_of_pos_events
            print 'update: ', i + 1, '/', self.nr_of_pos_events #self.nr_of_pos_events
            #sample user
            userID = self.sampleUser()

            if len(pos_per_user[userID]) == 0:
                pos_per_user[userID] = [(itemID, self.userItems[userID][0][2])]
                for i in range(1, len(self.userItems[userID])):
                    pos_per_user[userID].append((self.userItems[userID][i][0], self.userItems[userID][i][2]))

            if userID == None:
                for i in range(1, len(pos_per_user)):
                    print 'user: ', i ,', len = ', len(pos_per_user[i])
                continue
            #sample positive item
            if not pos_per_user[userID]:
                continue
            pos_event = random.choice(pos_per_user[userID])
            pos_item = pos_event[0]
            if pos_item not in self.feat:
                continue
            voteTime = pos_event[1]
            voteTime = int(voteTime)
            # print 'voteTime = ', voteTime
            epoch  = self.timeInEpoch(voteTime)
            # print 'epoch = ', epoch
            pos_per_user[userID].remove(pos_event)

            #sample negative item
            # creating the list of all pos_items of userID
            pos_item_of_userID = []
            for i in range(len(self.userItems[userID])):
                item_id = self.userItems[userID][i][0]
                pos_item_of_userID.append(item_id)

            neg_item = self.sample_neg_item(pos_item_of_userID)
            if neg_item not in self.feat:
                continue

            #update factors
            self.updateFactors(userID, pos_item, neg_item, epoch)

    # updating factors
    def updateFactors(self, userID, pos_item, neg_item, epoch):

        pos_feat = self.feat[pos_item].toarray()
        neg_feat = self.feat[neg_item].toarray()
        pos_feat = pos_feat[0]
        neg_feat = neg_feat[0]

        feat_i = [] # the features of the pos_item
        feat_j = [] # the features of the neg_item
        for i in range(4096):
            feat_i.append((i, pos_feat[i]))
            feat_j.append((i, neg_feat[i]))

        diff = []
        #sparse representation
        p_i = 0
        p_j = 0
        while p_i < len(pos_feat) and p_j < len(neg_feat):
            ind_i = feat_i[p_i][0]
            ind_j = feat_j[p_j][0]
            if ind_i < ind_j:
                diff.append((ind_i, feat_i[p_i][1]))
                p_i = p_i + 1
            elif ind_i > ind_j:
                diff.append((ind_j, feat_j[p_j][1]))
                p_j = p_j + 1
            else:
                diff.append((ind_i, feat_i[p_i][1] - feat_j[p_j][1]))
                p_i = p_i + 1
                p_j = p_j + 1
        while p_i < len(feat_i):
            diff.append(feat_i[p_i])
        while p_j < len(feat_j):
            diff.append((feat_j[p_j][0], - feat_j[p_j][1]))
        
    # print 'epoch', epoch
        len_of_diff = len(diff)
        # E * (x_i - x_j)
        theta_i = np.zeros(self.K2)
        theta_i_per_bin = np.zeros(self.K2)
        start_theta = time.time()
        for r in range(self.K2):
            for ind in range(len_of_diff):
                c = diff[ind][0]
                feat_val = diff[ind][1]

                theta_i[r] += self.E[r][c] * feat_val
                theta_i_per_bin[r] += self.E_t[epoch][r][c] * feat_val
        end_theta = time.time()
        print 'theta_i_time = ', end_theta - start_theta

        visual_score = 0
        for k in range(self.K2):
            visual_score += self.theta_user[userID][k] * (theta_i[k] * self.J_t[epoch][k] + theta_i_per_bin[k])
    
    # print 'visual score = ', visual_score

        visual_bias = 0
        for ind in range(len_of_diff):
            c = diff[ind][0]
            visual_bias += (self.betta_cnn[c] * self.C_t[epoch][c] +  self.betta_cnn_t[epoch][c]) * diff[ind][1]


        # x_uij = prediction(user_id, pos_item_id, bin) - prediction(user_id, neg_item_id, bin);

        pos_i = self.itemIdToInt[pos_item]
        neg_i = self.itemIdToInt[neg_item]

        bi = self.b_i[pos_i]
        bj = self.b_i[neg_i]

        x_uij = bi - bj
        x_uij += np.inner(self.gamma_user[userID], self.gamma_item[pos_i]) - np.inner(self.gamma_user[userID], self.gamma_item[neg_i])
        x_uij += visual_score + visual_bias

        deri = 1/(1 + np.exp(x_uij))


        self.b_i[pos_i] += 0.005 * (deri - 1 * bi)
        self.b_i[neg_i] += 0.005 * (-deri - 1 * bj)

        # updating latent factors
        start_non_vf = time.time()
        for k in range(self.K):
            uf = self.gamma_user[userID][k]
            _if = self.gamma_item[pos_i][k]
            _jf = self.gamma_item[neg_i][k]

            self.gamma_user[userID][k] += 0.005 * (deri * (_if - _jf) - 1 * uf)
            self.gamma_item[pos_i][k] += 0.005 * (deri * uf - 1 * _if)
            self.gamma_item[neg_i][k] += 0.005 * (-deri * uf - 1/10.0 * _jf)
        end_non_vf = time.time()
        time_elapsed_non_vf = start_non_vf - end_non_vf
        # print 'time elapsed for non visual factors: ', time_elapsed_non_vf, ' sec.'

        # updating visual factors
        start_vf = time.time()
        for k2 in range(self.K2):
            v_uf = self.theta_user[userID][k2]
            j_t = self.J_t[epoch][k2]

            for ind in range(len_of_diff):
                c = diff[ind][0]
                common = deri * v_uf * diff[ind][1]

                self.E[k2][c] += 0.005 * (common * j_t)
                self.E_t[epoch][k2][c] += 0.005 * (common - 0.0001 * self.E_t[epoch][k2][c])

            self.theta_user[userID][k2] += 0.005 * (deri * (theta_i[k2] * j_t + theta_i_per_bin[k2]) - 1 * v_uf)
            self.J_t[epoch][k2] += 0.005 * (deri * theta_i[k2] * v_uf - 0.0001 * j_t)

        for ind in range(len_of_diff):
            c = diff[ind][0]
            c_tf = self.C_t[epoch][c]
            b_cnn = self.betta_cnn[c]
            common = 0.005 * deri * diff[ind][1]

            self.betta_cnn[c] += common * c_tf
            self.C_t[epoch][c] += common * b_cnn - 0.005 * 0.0001 * c_tf
            self.betta_cnn_t[epoch][c] += common - 0.005 * 0.0001 * self.betta_cnn_t[epoch][c]
        end_vf = time.time()
        time_elapsed_vf = end_vf - start_vf
        print 'time elapsed on visual factors: ', time_elapsed_vf,' sec.'
    # sample user
    def sampleUser(self):
        userId_ = randint(1, self.nUsers)

        return userId_

    #sample negative item
    def sample_neg_item(self, pos_per_user):
        while True:
            neg_item = random.choice(self.list_of_items)
            if neg_item not in pos_per_user:
                return neg_item

    def calBin(self, time_st):
        interval = (self.maxTime - self.minTime) / self.nBins
        bin_ind = np.minimum(self.nBins - 1, int((time_st - self.minTime)/interval))

        return bin_ind

    # calculate the corresponding epoch given timestamp
    def timeInEpoch(self, timesta):
        inte = (self.maxTime - self.minTime)/80
        # print 'interval = ', inte
        b_ind = np.minimum(79, int((timesta - self.minTime)/inte))
        # print 'b_ind =', b_ind
        for i in range(len(self.epochs)):
            start_bin = self.epochs[i][0]
            end_bin = self.epochs[i][1]
            if end_bin >= b_ind:
        # print 'epochs ==', self.epochs
        # print 'epoch_ind = ', i
                return i

    # calculate pos_item_per_bin
    def pos_item_per_bin(self):
        votes_per_bin = []
        for i in range(80):
            votes_per_bin.append([])

        # adding the samples from the validation set to the corresponding bin
        for k,v in self.val_per_user.items():
            user = k
            item = self.val_per_user[k][0]
            rating = self.val_per_user[k][1]
            voteTime = self.val_per_user[k][2]
            interv = (max(times_) - min(times_))/80
            # print 'interval = ', inte
            b_ind = np.minimum(79, int((voteTime - min(times_))/interv))
            votes_per_bin[b_ind].append((user, item))

        return votes_per_bin

    # epoch initialization
    def init_epoch(self):
        epochs = []
        interval = 80/10
        bin_from = 0
        bin_to = interval - 1
        for i in range(10):
            if epochs == []:
                epochs.append((bin_from, bin_to))
            else:
                bin_from = bin_to + 1
                bin_to = bin_to + interval
                epochs.append((bin_from, bin_to))

        return epochs

    # DP
    def DP(self, num_of_neg_items):
        pos_per_user = self.pos_per_user_()
        sampleMap = {}
        for k,v in self.userItems.items():
            user = k
            for i in range(num_of_neg_items):
                neg_item = self.sample_neg_item(pos_per_user[user])
                if user not in sampleMap:
                    sampleMap[user] = [neg_item]
                else:
                    sampleMap[user].append(neg_item)

        # apply DP
        fval = self.f(0, 79, 0, 10, sampleMap)
        print 'f() = ', fval

        new_epochs = []
        start = 0
        end = 79
        ep = 0
        pieces = 10
        last_bin_to = -1

        for i in range(10):
            seprator = self.sol[start][end][ep][pieces - 1]

            if seprator == -1:
                print 'Exception: No solution found by DP'

            if new_epochs == []:
                binFrom = last_bin_to + 1
                binTo = last_bin_to = seprator
                new_epochs.append((binFrom, binTo))
            else:
                binFrom = last_bin_to + 1
                binTo = last_bin_to = seprator
                new_epochs.append((binFrom, binTo))

            start = seprator + 1
            pieces = pieces - 1
            ep += 1
        
        print 'epochs = ', self.epochs
        self.epochs = new_epochs
        print 'new_epochs = ', self.epochs
       

    # positive items per user
    def pos_per_user_ (self):
        pos_per_user = {}
        for k,v in self.userItems.items():
            for i in range(len(self.userItems[k])):
                item__ = self.userItems[k][i][0]
                if k not in pos_per_user:
                    pos_per_user[k] = [item__]
                else:
                    pos_per_user[k].append(item__)

        return pos_per_user

    # f()
    def f(self, startBin, endBin, epo, pieces, sample_map):
        if self.memo[startBin][endBin][epo][pieces - 1] != sys.float_info.max:
            return self.memo[startBin][endBin][epo][pieces - 1]

        if pieces == 1:
            self.memo[startBin][endBin][epo][0] = self.onePieceVal(startBin, endBin, epo, sample_map)
            if self.memo[startBin][endBin][epo][0] < sys.float_info.max:
                self.sol[startBin][endBin][epo][0] = endBin
            else:
                self.sol[startBin][endBin][epo][0] = -1
            return self.memo[startBin][endBin][epo][0]

        max_val = -sys.float_info.max
        for k in range(startBin, endBin - pieces):
            val = self.f(startBin, k, epo, 1, sample_map) + self.f(k + 1, endBin, epo + 1, pieces - 1, sample_map)
            if val > max_val:
                max_val = val
                self.sol[startBin][endBin][epo][pieces - 1] = k
        self.memo[startBin][endBin][epo][pieces - 1] = max_val
        return max_val

    def onePieceVal(self,startBin, endBin, epo, sampleMap):
        res = 0
        total = 0
        for i in range(startBin, endBin + 1):
            if self.memo[i][i][epo][0] != sys.float_info.max:
                res += self.memo[i][i][epo][0]
                continue
            for j in range(len(self.votes_per_bin[i])):
                user_ = self.votes_per_bin[i][j][0]
                item_ = self.votes_per_bin[i][j][1]
                item_id_int = self.itemIdToInt[item_]
                x_ui = self.prediction(user_, item_id_int, epo)

                for k in range(len(sampleMap[user_])):
                    neg_item = sampleMap[user_][k]
                    neg_item_ = self.itemIdToInt[neg_item]
                    x_uj = self.prediction(user_, neg_item_, epo)

                    total += np.log(self.sigmoid(x_ui - x_uj))

            self.memo[i][i][epo][0] = total
            self.sol[i][i][epo][0] = i
            res += total

        return res

    # sigmoid function
    def sigmoid(self, x):
        sig = 1 / (1 + np.exp(-x))
        return sig

    # DP init
    def dp_init(self):
        memo = np.zeros((80,80,10,10))
        sol = np.zeros((80,80,10,10))
        for b in range(80):
            for j in range(80):
                for k in range(10):
                    for x in range(10):
                        memo[b][j][k][x] = sys.float_info.max # not calculated
                        sol[b][j][k][x] = -1 # not calculated
        return memo, sol

    def getVisualFactors(self):
        for bin in range(10):

            visual_scores = []
            dim0 = []
            dim1 = []
            dim2 = []
            dim3 = []
            dim4 = []
            dim5 = []
            dim6 = []
            dim7 = []
            dim8 = []
            dim9 = []
            dim10 = []
            dim11 = []
            dim12 = []
            dim13 = []
            dim14 = []
            dim15 = []
            dim16 = []
            dim17 = []
            dim18 = []
            dim19 = []

            for i in range(len(self.list_of_items)):
                asin = self.list_of_items[i]
                itemID = self.itemIdToInt[asin]
                if asin not in feat:
                    continue
                item_feat = self.feat[asin].toarray()
                item_feat = item_feat[0]

                for k in range(self.K2):
                    for f in range(4096):
                        self.theta_item_per_bin[bin][itemID][k] += (self.E[k][f] * self.J_t[bin][k] + self.E_t[bin][k][f]) * item_feat[f]

                # visual bias
                for f in range(4096):
                    self.betta_item_visual_per_bin[bin][itemID] += (self.betta_cnn[f] * self.C_t[bin][f] + self.betta_cnn_t[bin][f]) * item_feat[f]

                dim0.append((asin, self.theta_item_per_bin[bin][itemID][0]))
                dim1.append((asin,self.theta_item_per_bin[bin][itemID][1]))
                dim2.append((asin,self.theta_item_per_bin[bin][itemID][2]))
                dim3.append((asin,self.theta_item_per_bin[bin][itemID][3]))
                dim4.append((asin,self.theta_item_per_bin[bin][itemID][4]))
                dim5.append((asin,self.theta_item_per_bin[bin][itemID][5]))
                dim6.append((asin,self.theta_item_per_bin[bin][itemID][6]))
                dim7.append((asin,self.theta_item_per_bin[bin][itemID][7]))
                dim8.append((asin,self.theta_item_per_bin[bin][itemID][8]))
                dim9.append((asin,self.theta_item_per_bin[bin][itemID][9]))
                dim10.append((asin,self.theta_item_per_bin[bin][itemID][10]))
                dim11.append((asin,self.theta_item_per_bin[bin][itemID][11]))
                dim12.append((asin,self.theta_item_per_bin[bin][itemID][12]))
                dim13.append((asin,self.theta_item_per_bin[bin][itemID][13]))
                dim14.append((asin,self.theta_item_per_bin[bin][itemID][14]))
                dim15.append((asin,self.theta_item_per_bin[bin][itemID][15]))
                dim16.append((asin,self.theta_item_per_bin[bin][itemID][16]))
                dim17.append((asin,self.theta_item_per_bin[bin][itemID][17]))
                dim18.append((asin,self.theta_item_per_bin[bin][itemID][18]))
                dim19.append((asin,self.theta_item_per_bin[bin][itemID][19]))

                vp = 0

                for u in range(1, 4):
                    vp += np.inner(self.theta_user[u], self.theta_item_per_bin[bin][itemID])
                vp = vp/4
                visual_scores.append((asin, vp))

            max_vs = max(visual_scores, key=operator.itemgetter(1))

            print 'itemID with max. visual score: ', max_vs[0],' visualScore = ', max_vs[1]

            for d in range(self.K2):
                if d == 0:
                    max_value = max(dim0, key=operator.itemgetter(1))
                    asin_ = max_value[0]
                    value_ = max_value[1]
                    print 'dim:',d,', itemID: ', asin_, ', value = ', value_


                if d == 1:
                    max_value = max(dim1, key=operator.itemgetter(1))
                    asin_ = max_value[0]
                    value_ = max_value[1]
                    print 'dim:',d,', itemID: ', asin_, ', value = ', value_

                if d == 2:
                    max_value = max(dim2, key=operator.itemgetter(1))
                    asin_ = max_value[0]
                    value_ = max_value[1]
                    print 'dim:',d,', itemID: ', asin_, ', value = ', value_

                if d == 3:
                    max_value = max(dim3, key=operator.itemgetter(1))
                    asin_ = max_value[0]
                    value_ = max_value[1]
                    print 'dim:',d,', itemID: ', asin_, ', value = ', value_

                if d == 4:
                    max_value = max(dim4, key=operator.itemgetter(1))
                    asin_ = max_value[0]
                    value_ = max_value[1]
                    print 'dim:',d,', itemID: ', asin_, ', value = ', value_

                if d == 5:
                    max_value = max(dim5, key=operator.itemgetter(1))
                    asin_ = max_value[0]
                    value_ = max_value[1]
                    print 'dim:',d,', itemID: ', asin_, ', value = ', value_

                if d == 6:
                    max_value = max(dim6, key=operator.itemgetter(1))
                    asin_ = max_value[0]
                    value_ = max_value[1]
                    print 'dim:',d,', itemID: ', asin_, ', value = ', value_

                if d == 7:
                    max_value = max(dim7, key=operator.itemgetter(1))
                    asin_ = max_value[0]
                    value_ = max_value[1]
                    print 'dim:',d,', itemID: ', asin_, ', value = ', value_

                if d == 8:
                    max_value = max(dim8, key=operator.itemgetter(1))
                    asin_ = max_value[0]
                    value_ = max_value[1]
                    print 'dim:',d,', itemID: ', asin_, ', value = ', value_

                if d == 9:
                    max_value = max(dim9, key=operator.itemgetter(1))
                    asin_ = max_value[0]
                    value_ = max_value[1]
                    print 'dim:',d,', itemID: ', asin_, ', value = ', value_

                if d == 10:
                    max_value = max(dim10, key=operator.itemgetter(1))
                    asin_ = max_value[0]
                    value_ = max_value[1]
                    print 'dim:',d,', itemID: ', asin_, ', value = ', value_

                if d == 11:
                    max_value = max(dim11, key=operator.itemgetter(1))
                    asin_ = max_value[0]
                    value_ = max_value[1]
                    print 'dim:',d,', itemID: ', asin_, ', value = ', value_

                if d == 12:
                    max_value = max(dim12, key=operator.itemgetter(1))
                    asin_ = max_value[0]
                    value_ = max_value[1]
                    print 'dim:',d,', itemID: ', asin_, ', value = ', value_

                if d == 13:
                    max_value = max(dim13, key=operator.itemgetter(1))
                    asin_ = max_value[0]
                    value_ = max_value[1]
                    print 'dim:',d,', itemID: ', asin_, ', value = ', value_

                if d == 14:
                    max_value = max(dim14, key=operator.itemgetter(1))
                    asin_ = max_value[0]
                    value_ = max_value[1]
                    print 'dim:',d,', itemID: ', asin_, ', value = ', value_

                if d == 15:
                    max_value = max(dim15, key=operator.itemgetter(1))
                    asin_ = max_value[0]
                    value_ = max_value[1]
                    print 'dim:',d,', itemID: ', asin_, ', value = ', value_

                if d == 16:
                    max_value = max(dim16, key=operator.itemgetter(1))
                    asin_ = max_value[0]
                    value_ = max_value[1]
                    print 'dim:',d,', itemID: ', asin_, ', value = ', value_

                if d == 17:
                    max_value = max(dim17, key=operator.itemgetter(1))
                    asin_ = max_value[0]
                    value_ = max_value[1]
                    print 'dim:',d,', itemID: ', asin_, ', value = ', value_

                if d == 18:
                    max_value = max(dim18, key=operator.itemgetter(1))
                    asin_ = max_value[0]
                    value_ = max_value[1]
                    print 'dim:',d,', itemID: ', asin_, ', value = ', value_

                if d == 19:
                    max_value = max(dim19, key=operator.itemgetter(1))
                    asin_ = max_value[0]
                    value_ = max_value[1]
                    print 'dim:',d,', itemID: ', asin_, ', value = ', value_

    def prediction(self, userID, itemID, epoch_):

        pred = self.b_i[itemID] + np.dot(self.gamma_user[userID], self.gamma_item[itemID]) +  np.dot(self.theta_user[userID], self.theta_item_per_bin[epoch_][itemID]) + self.betta_item_visual_per_bin[epoch_][itemID]
        # np.dot(self.gamma_user[userID], self.gamma_item[itemID])
    return pred

    def AUC_ (self, test_per_us, val_per_us):

        AUC_  = np.zeros(self.nUsers + 1)
        bin_indices = []
        for k,v in test_per_us.items():
            user_ = k
            # print 'USER: ', user_, ' being tested...'
            test_item_asin = test_per_us[k][0]
            val_item_asin = val_per_us[k][0]

            if test_item_asin not in self.feat:
                continue
            # print test_item_asin

            item_intID = self.itemIdToInt[test_item_asin]

            time_d = int(test_per_us[k][2])
            # print test_per_us[k]
            # print time_d
            # bin_ind = self.calBin(time_d)

            epoch = self.timeInEpoch(time_d)
            # print time_d
            # print 'bin ind = ', bin_ind
            bin_indices.append(bin_ind)
            pred_of_test = self.prediction(user_, item_intID, epoch)


            asins_of_user = []
            for a in range(len(self.userItems[user_])):
                asins_of_user.append(self.userItems[user_][a][0])

            count = 0
            count_val = 0
            maxx  = 0.0
            for i in range(len(self.list_of_items)):
                asin = self.list_of_items[i]
                item_id = self.itemIdToInt[asin]
                if asin not in self.feat:
                    continue
                if asin in asins_of_user or asin == test_item_asin or asin == val_item_asin:
                    continue
                else:
                    maxx += 1
                    pred_of_neg = self.prediction(user_, item_id, epoch)

                    if pred_of_test > pred_of_neg:
                        count += 1

            AUC_[user_] = 1 * (count/maxx)

            # print 'count = ', count
            # print 'max =', maxx
             # print 'AUC for userID: ', user_,' is: ', AUC_[user_]

        auc = 0
        num_users = len(test_per_us)
        # print 'users = ', num_users

        for i in range(len(AUC_)):
            auc += AUC_[i]

        # print 'AUC = ', auc/num_users
        # print 'bins = ', bin_indices
        print 'auc = ', auc, ', num_users = ', num_users
    # print 'DP applied!'
        return auc/num_users

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